Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Kuala Lumpur to Montevideo as you normally would.
Montevideo Carrasco (MVD) is the airport you will fly into if you book a flight from Kuala Lumpur to Montevideo. You should not have trouble finding flights to Carrasco from Kuala Lumpur; the airport handles an average of 0 inbound flights from Kuala Lumpur per day. You should also have plenty of airline options to choose from since 1 airline has flights to the Montevideo airport from Kuala Lumpur. It is only a 16.1 km journey from Carrasco (MVD) to Montevideo’s city centre.